Logic Masters Deutschland e.V.

My first 6×6×6 linked puzzles, a tribute to zetamath's Vignettes and the doubler craze. Soon after seeing Vignettes and setting my first modifier puzzle, I started thinking about how to take the concept of modifier cells to its limit.

The answer came to me like twisted murmurings of an eldritch god: a linked 6×6×6, six modifiers involving six different mathematical operators, including a square root. I kept the idea on the shelf for a while, thinking no rational person would set such a thing. I joked about it to other setters until, eventually, enough people goaded me into doing it that I actually made the dang thing.

And so, here it is.

Rules

In each puzzle, place the digits 1-6 once in each row, column, and box.

In each puzzle, there are six modifier cells, one in each row, column, and box. There are six types of modifiers, each modifying the value of a digit for the purposes of clues. The modifiers apply the following operations to the digit n:

• n + 2 (n plus 2)
• n - 2 (n minus 2)
• n × 2 (n times 2)
• n ÷ 2 (n divided by 2)
• n² (n squared)
• √n (square root of n)

Each digit is modified once in each puzzle, and each modifier is used once in each puzzle. No two puzzles contain modifiers in the same cell. In addition, a modifier may only be applied to a specific digit once among all puzzles (e.g. if +2 is applied to 3 in one puzzle, it cannot be applied to 3 in any other puzzle).

The rules for the individual puzzles are:

1. Renban: Numbers on a purple line form a set of consecutive integers in any order.
2. Thermometer: Numbers on a thermometer strictly increase from the bulb.
3. Between lines: Numbers on a line are between its corresponding circles.
4. Whispers: Numbers on a green line have a difference of at least 3.
5. Kropki: Numbers separated by a black dot have a ratio of 1:2.
6. Arrows: Numbers on an arrow sum to the value in the circle.

In addition, a reference with all modifier values has been provided to aid in solving.